Voltage-controlled robust topological states in perforated beams

Topological metamaterials possess waveguiding and energy concentration properties even under perturbations such as defects or disorders. Tunable topological materials offer enhanced flexibility to these properties. In this study, a voltage-controlled strategy is presented to realize the tunable robust topological states. First, a perforated beam with piezoelectric patches and additional steel columns is proposed to analyze the topological properties, and the corresponding numerical model based on Timoshenko beam theory is introduced to analyze the band gap properties and transmission spectra by spectral element method (SEM). Then the effects of the applied voltage on the resonance frequency and equivalent stiffness of piezoelectric patches are characterized. Two new band gaps emerge around the locally resonant band gap and topological phase transition can be achieved by altering the collective displacement of the perforations and resonators. Subsequently, the finite element simulations are presented to validate the accuracy of SEM results, and the equivalent voltage-controlled stiffness is used in SEM to simplify the relationship between voltage and topological properties. The Zak phase calculations demonstrate the topological properties of opened band gaps and further indicate the existence of topologically protected interface states (TPISs). Finally, the transmission spectra are used to analyze the characteristics of TPISs, and the robustness of TPISs is examined by introducing different perturbation factors. The results show that the frequency of topological states can be simply tuned by varying the voltage on the piezoelectric patch, and the topological rainbow trapping can be realized in a designed gradient system without changing the geometric configuration.